**Reference:**

B. De Schutter and
B. De Moor,
"Minimal realization in the max algebra," Tech. rep. 94-29,
ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 29 pp., May 1994.

**Abstract:**

The main topic of this paper is the minimal realization problem in the
max algebra, which is one of the modeling frameworks that can be used
to model discrete event systems. First we determine necessary and for
some cases also sufficient conditions for a polynomial to be the
characteristic polynomial of a matrix in the max algebra. Then we show
how a system of multivariate max-algebraic polynomial equalities can
be transformed into an Extended Linear Complementarity Problem (ELCP).
Finally we combine these results to find all equivalent minimal state
space realizations of a single input single output (SISO) discrete
event system. We also give a geometrical description of the set of all
minimal realizations of a SISO max-linear discrete event system.

Technical report: pdf file (281 KB)

@techreport{DeSDeM:94-29,

author={B. {D}e Schutter and B. {D}e Moor},

title={{Minimal} realization in the max algebra},

number={94-29},

institution={ESAT-SISTA, K.U.Leuven},

address={Leuven, Belgium},

month=may,

year={1994}

}

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